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Vague quantification in the scientific journal article

David Banks
p. 17-27

Résumés

Bien que l’écriture scientifique soit en général considérée précise, elle contient un nombre significatif d’exemples de quantification imprécise. L’étude d’un petit corpus de six articles de recherche scientifique démontre que les expressions constituées uniquement de mots sont distribuées différemment par rapport aux expressions comprenant des chiffres. Dans certains cas, l’imprécision est compensée à l’intérieur même du texte. L’usage de la quantification imprécise est lié au phénomène de hedging. Il est possible que ces traits opèrent sur un gradient triangulaire des dispositifs de hedging.

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Texte intégral

Introduction

1Science is perceived as being a precise activity. Its principal activity is that of measurement, and measurement is a question of precise quantification. But not only is this the way that outsiders see scientific activity, it is the way scientists present it themselves; as Channell (1990) puts it,

Good academic writing is believed by its users to have characteristics of precision, detail, and accuracy. (Channell 1990: 95)

And one of the scientific authors represented in the corpus used in this study says,

...we have been developing methods to quantify stomach contents with acceptable accuracy and precision. (DeMartini 1996: 251)

2It will be noted, however, that the word acceptable is particularly significant in the context of what follows in this article, whose object is to consider the incidence of imprecision in the expression of quantification in the scientific journal article.

3Although this subject is linked to that of hedging (Salager-Meyer 1994, 1995), it has received comparatively little attention compared to other forms of hedging, such as modality, for example. Powell (1985) considered the deliberate use of vague quantifying expressions, but not specifically in scientific writing. Dubois (1987) studied imprecise numerical expressions in biomedical slide talks. She claims that in this genre measurements are always statistical in character. This presumes that measurements are of non-discrete entities, or are averages of discrete entities, otherwise this would not necessarily be the case. Moreover she points out that no matter how many decimal places are used in expressing a measurement, it is always a rounded form of the following decimal place; that is, for example, 8.342 means that the measurement was actually between 8.3415 and 8.3425. Figures which are ostensibly expressing that same quantities may have different effects; 23.0 is perceived as being more precise than 23. If all figures given are multiples of 5, they will be perceived as being correct to the nearest 5. She goes on to say,

The imprecise nature of many of the numbers used, which includes rounding, sometimes extreme rounding, hedges, and ranges without standard error or standard deviation, is additional evidence for placing them at the preinformational stage. If confirmation is needed, a look at the informational stage - journal article publication - reveals a higher order of precision in the use of numbers. (Dubois, 1987: 539)

4The object of this article is to see to what extent the scientific journal article exhibits a higher order of precision in the use of numbers.

5Perhaps the best-known work on vagueness in language is Channell 1994, but there is little that is of relevance to scientific writing in that book. Of greater interest for this subject is her earlier (1990) paper, in which she suggests a rhetorical structure in terms of: introduction, body of paper, conclusions. She then categorizes the introduction as being general and vague, the body of the paper as being particular and precise, and the conclusions, like the introduction, as being general and vague. She attempts to explain these phenomena by fitting them into a Gricean mould (Grice 1975). Myers (1996) also discusses this type of language in pragmatic terms, in which Grice’s maxims play a significant part.

The corpus

6In order to look at this question and also to see whether there are any differences between the ultra-hard sciences like particle physics, and the not-so-hard sciences like marine biology, I have studied a small corpus of six scientific journal articles, three from the ultra-hard sector, and three from the not-so-hard sector. All were published in 1996.

7On Swales’ scale for estimating the probability of authors of scientific journal articles being native speakers (Swales 1985), which goes from +12 to -12, five of these articles scored between +9 and +12, two having the maximal score. These are classed as native speaker in Swales’ system. One of the articles had a score of +3, which counts as probably native speaker. However it should be pointed out that the comparatively low score is due more to absence of information, than the presence of negative information.

Frequency

  • 1 Articles in the corpus are identified by the first named author.

8For the purposes of this study, a rhetorical analysis in terms of introduction (I), methods (M), results (R) and discussion (D), has been used. This analysis is unproblematical for the not-so-hard scientific articles in the sample, as these four terms were used as section headings and were accepted as such. The ultra-hard articles were a little more difficult in that the heading Results and Discussion was used for a single section. In Tapsak1 this section is basically results with virtually no discussion; in Shear there is a fairly clear division between the part where the results are given and that where they are discussed; in Lindsay this section is mainly a discussion section, the results being given to some extent in the methods section.

9The estimated frequency of vague quantifying expressions (no. of words per expression) is as in Table 1.

Table 1. Number of words per expression

I

M

R

D

Overall

Shelton

55

58

41

44

48

Lesser

48

780

83

43

68

DeMartini

27

49

29

61

42

Tapsak

57

-

168

-

79

Shear

60

100

29

58

44

Lindsay

-

100

-

73

93

10It will be noted that there were no examples in the introduction section of Lindsay, nor in the methods section of Tapsak. The comparatively high figure (i.e., low frequency) for the methods section of Lesser is due to there being only one example in this section.

11If it is accepted that the mid-point of the overall figures for individual articles is ~60, then two of the not-so-hard scientific papers are under this figure, whereas two of the ultra-hard scientific papers are over this figure. To the extent that the results from such a small sample are significant this provides the working hypothesis that there is a two to one chance of the frequency of vague quantifying expressions being more frequent (less than 60 words of text per expression) for the not-so-hard sciences, and less frequent (more than 690 words of text per expression) for the ultra-hard sciences.

12The results provide no hard evidence for the hypothesis that vague quantifying expressions are more frequent in introductions than in other sections of the article.

  • 2 Highlighting in examples is mine throughout.

13There appear to be significant differences between those expressions which are composed only of words, and those which are composed of figures only or combinations of words and figures. The following are examples of the first type:2

The eyes have large apertures, tapeta and rhebdoms with large cross-sectional areas. (Shelton 391)

High incidence of total regurgitation will be more likely to overwhelm size biases in retention and therefore lower precision. (DeMartini 255)

Unfortunately, acetylation of PE and its oligomers is a slow process. (Tapsak 1687)

In other instances, florogenic derivatives have relatively small Stokes shifts, making it difficult to discriminate fluorescence from elastic and inelastic scatter without sacrificing a large fraction of the fluorescence signal. (Shear 1778)

and the following are examples of the second type:

The photon flux of the adapting light at the eye was adjusted to be ~1 log unit below that of the unattenuated test flashes. (Shelton 394)

Briefly the chambers have a volume of 2 l and are approximately 15 cm in diameter. (Lesser 172)

The errors in the absolute cross section values depend, in addition, on uncertainties in the published two-photon cross sections for fluoresein and the fluorescence quantum yields and, consequently, are likely ±50%. (Shear 1781)

The gas target typically comprised approximately 74% molecular oxygen, 24% atomic oxygen, 1.5% water vapor; and 0.5% molecular nitrogen and carbon monoxide. (Lindsay 215)

14If frequencies for those expressions with words only and those with figures are compared, then the following is found as shown in Table 2.

Table 2

I

M

R

D

word

figure

word

figure

word

figure

word

figure

Shelton

12

-

5

12

14

1

31

3

Lesser

10

1

-

1

4

7

22

2

DeMartini

9

2

8

10

6

16

14

2

Tapsak

15

1

-

-

4

-

Shear

14

3

-

8

17

41

9

3

Lindsay

-

-

20

10

12

-

Total

60

7

33

41

45

65

88

10

15These figures show that in the introduction and discussion sections there is a fairly strong tendency to use expressions containing words only. The ratio is 8.6:1 for the introduction and 8.8:1 for the discussion section. In the methods and the results sections there is a tendency, but in this case only a slight tendency, to prefer expressions incorporating figures. The ratio for the methods section is 1.2:1 and for the results section 1.4:1. It may well be this that lies behind the vague-precise-vague structure that Channell perceived, that is vague is the outer sections, introduction and discussion, and precise in the central sections, methods and results, though here we see that the perceived precision of the central sections is merely relative.

Grammatical function

16Consideration of the grammatical function of those expressions that are made up of words only indicates that, as might be expected, 66% are modifiers. The most common (with between 10 and 20 examples in the corpus) are large(r), small(er), high(er), low(er) and significant. The following are corpus examples:

Reflecting superposition eyes with their large apertures, large rhabdoms and diffusely reflecting tapeta are clearly adapted to increase absolute sensitivity. (Shelton 397)

... further, this result allows us to predict that subsequent increases in UV-B radiation, due to even small incremental decreases in stratospheric ozone, may have demonstrable effects on the productivity of this shallow-water coral and possibly other species. (Lesser 175)

However, the low volatility of PE, di-PE, and the higher molecular weight PE oligomers does not permit their direct analysis. (Tapsak 1685)

During this time collisional and radiative effects lead to a significant reduction in the excited-state contamination of the target. (Lindsay 213)

17Next in order of importance, but far behind, are subject complements (or attributive adjectives or copula complements) which account for 14%. Those that occur several times are small(er), low(er), similar and significantly used as a submodifier within a subject complement. The following are corpus examples:

Indeed, more recent data from a variety of terrestrial species with refracting superposition eyes has shown that in some cases resolution is not significantly worse than that found in apposition eyes ... (Shelton 391)

Where the resulting aperture is relatively small, as in the light-adapted eye of C. destructor, the amount of defocusing will also be small. (Shelton 398)

Although these cross sections are significantly lower than the peak cross sections of fluorescein (~40 GM) and rhodamine B (~300 GM), the fluorogenic species examined in these studies could be excited efficiently at moderate excitation powers, even when the laser beam was focused with a low NA objective. (Shear 1781)

18Adjuncts account for 9%, and those that occur more than once are usually, widely, significantly and to the nearest ... Examples include:

Usually data was obtained only for the middle region of the sigmoid curve. (Shelton 395)

Gas chromatography (GC) has been widely used. (Tapsak 1685)

Although MPE fluorescence measurements of fluorogen derivatives will offer the best detection limits when used with a separation procedure, applications that do not rely on separations also benefit significantly from multiphoton excitation. (Shear 1783)

The eviscerated wet weight (EW) of each snapper was recorded to the nearest gram. (DeMartini 251)

19Nouns account for 6%, and those occurring more than once are increase, decrease and (over/under)estimate. Examples include:

Any inhibition of photosynthesis by an increase in UV radiation may effect carbon flux through the shikimic acid pathway and result in still lower concentrations of MAZAs and an increase in the biological effectiveness of UV radiation for corals. (Lesser 176)

Adjusted bootstrapped estimates thus were slightly larger than the bootstrapped estimates from unadjusted data. (DeMartini 253)

20Verbs accounted for 3%, and those that occurred more than once were decrease, (under)estimate, exceed and average. Examples include:

Laboratory conditions, despite the enhanced UV-B component, may actually underestimate the biological effectiveness of UV radiation in the field, but can still provide important insight into mechanisms of damage caused by UV radiation. (Lesser 175)

Divers observed fish - underwater visibilities consistently exceeded 30 m - as they were reeled up to 15-18 m and subsequently to the sea surface ... (DeMartini 251)

The positive relation between fish size and prey volume was associated with snapper growth; juveniles averaged 50% greater body weight at the end versus the beginning of the 7-month period of study. (DeMartini 253)

21Qualifiers (postmodifiers) were comparatively rare, being used by only one of the authors in the sample, and accounted for 1% of the total.

Mathematical expressions

22The prototypical vague quantifying expression, about/approximately x, was comparatively rare; there were only twelve examples in the corpus, of which the following are examples:

The relatively short target cell length, approximately 1 mm, ensures that the scattering occurs within a very well defined location, thereby enabling accurate definition of the scattering angles of the neutral products. (Lindsay 213)

The gas target typically comprised approximately 74% molecular oxygen, 24% atomic oxygen 1.5% water vapor, and 0.5% molecular nitrogen and carbon monoxide. (Lindsay 215)

Juvenile snapper were caught by hook and line from near-bottom depths of 60-90 m, about 3-4 km off-shore of Kaneohe Bay, windward Oahu, Hawaii, on nine dates during the period February-August 1994. (DeMartini 251)

The determined variability in the results at individual wavelengths was approximately 10%. (Shear 1781)

23However, the mathematical equivalent of this, ~x, was much more common, with 36 examples in the corpus. There were also 17 examples of mathematical expression of range, in the form X-Y, as well as the written expression between x and y which occurred 3 times, and from x to y, which occurred once. There were 14 examples of mathematical expression of relative size, <, >, ≤, ≥, and the expressions no more than x, did not exceed x, up to x, and at, and above x occurred once each. The mathematical expression for approximate equality, ≈, occurred 7 times, and the symbol ± occurred 5 times. On six occasions there was some indication of the application of statistical tests. The following are examples of these phenomena:

This excitation/collection geometry should yield ~0.05 count/molecule, and assuming that no additional background exists, ~300 molecules of CPP-bradykinin are needed to achieve a signal-to-noise ratio of 1 (i.e., a signal of 15 counts). (Shear 1782)

Divers witnessed unbagged snapper frequently regurgitating stomach contents between 15-18 m depth and the sea surface, as the volume of gases in swimbladders expanded by more than an atmosphere of pressure, equivalent to 40% of all bladder expansion between depths of 75 and 15 m. (DeMartini 252)

In the absence of cellular autofluorescence in overlapping spectral regions, the MPE fluorescence detection limit for such applications is estimated to be <104molecules when using a 1.3 NA objective to collect fluorescence – a level that is still more than 10-fold lower than the best reported fluorogen mass detection limits using single-photon excitation. (Shear 1783)

For mode-locked femto-second Ti-sapphire lasers, g2 104-105. (Shear 1779)

From bagged snapper, we collected an average 108% more prey (0.75 ±0.57 mL [SD], versus 0.36 ±0.24 mL for unbagged fish) ... (DeMartini 252)

Compensation

24Some of the more interesting examples in the corpus exhibited a phenomenon which I shall call compensation. This occurred when a vague quantifying expression was accompanied by precise figures in the article. This was sometimes done within the text itself, as in:

However, when the readings were made with the eye immersed, the light-adapted value of 8.85° was significantly less than the dark-adapted value of 11.30°. (Shelton 396)

Few bagged (n=3) and unbagged (n=3) snapper had ruptured swimbladders, and both bagged and unbagged fish had equivalently high indices of stomach eversion (Table 1). (DeMartini 252)

Three-photon excitation via this UV-accessible state is expected to cause a greater positive deviation of the measured slope when the two-photon cross section is small, as is the case at 713 nm. (Shear 1781)

A greater relative frequency of nekton for bagged (25%) versus unbagged (14%) snapper was only suggestive (P=0.06; Fig. 2). (DeMartini 253)

Tri-PE is practically insoluble at ambient temperature and only slightly soluble at 100°C, 0.5 g/100 g of water. (Tapsak 1685)

25In the first of these examples one could well imagine the light-adapted value was significantly less than the dark adapted value. This would have been a normal vaguely quantified expression, but the addition of precise figures for the values, of 8.85°, of 11.30° compensates the vagueness of the expression. Similarly, in the second of these examples few is vague but the exact figure, n=3, is given in brackets. In the third example small is compensated by the expression as is the case at 713 nm. The vague greater relative frequency of the fourth example is made precise with the two frequencies, 25% and 14% given in brackets. And in the final example we are told that slightly soluble is in this case 0.5g/100g of water. In other cases the compensation was effected by giving exact figures for a vague expression in the form of a table or graphic representation.

26There is something peculiar about this vagueness of expression when in fact the scientist is ultimately being precise. It suggests that vagueness is perceived as having a value of its own, that even in being precise, vague quantifying expressions are a valid, and perhaps even a necessary, element in the writing. This fits in with the question of hedging which I should now like to consider in this context.

Hedging

27I think it is important to distinguish hedging from hedging devices. Crompton (1997) says:

A hedge is an item of language which a speaker uses to... (Crompton 1997: 281)

28But the hedge is precisely the use which the speaker makes of the language item, rather than the item itself. Salager-Meyer (1994) includes “approximators” in her taxonomy and goes on to say:

... even though not all approximators serve to make things vague —some are indeed used when exact figures are irrelevant or unavailable or when the state of knowledge does not allow the scientist to be more precise— they were all recorded as “hedges”. (Salager-Meyer 1994: 154)

29In other words, she recognizes this difference, but what she then goes on to study are hedging devices, that is linguistic expressions that can be used as hedges, but are not necessarily hedges. In previous work (Banks 1994a, 1994b), I have suggested that there are (at least) three different reasons for using a hedging device:

  • to express incomplete or inconclusive data.

  • to conform to expected style.

  • to avoid face threatening behaviour.

30I would suggest that the phenomenon of compensation which was discussed above falls into the second of these categories. That is, even where the vague expression is not strictly necessary it is used because it conforms to the style which is expected. There is thus a certain institutionalization of particular linguistic traits.

31It is my feeling that those examples in the corpus which are composed of figures only (as opposed to words and figures) probably fall into the first category. That is the vagueness results from the nature of the data available. In other cases, it could be any of the three categories that is in question, or a mixture of more than one. It may be the case (I suspect it is) that we are here dealing with a 3-way cline, and it may be difficult, particularly for the non-specialist to place an individual example on the cline. However consideration of the following examples may be indicative.

Laboratory conditions, despite the enhanced UV-B component, may actually underestimate the biological effectiveness of UV radiation in the field, but can still provide important insight into mechanisms of damage caused by UV radiation. (Lesser 1996: 175)

32This seems close to a genuine hedge. One might note the presence of another hedging device, may, thus constituting what I have elsewhere called a fertilized hedge (Banks 1994b). One might also notice the generally defensive nature of the co-text.

Consequently, efficient two-photon excitation is achieved using lasers that provide brief (~100 fs), high-intensity pulses approximately once per several fluorescence lifetimes of the fluorphore. (Shear 1996: 1779)

33This appears to be a hedge, but it is mitigated to some extent by at least part of the vague quantification being compensated. I suspect that it was difficult for the researcher to be more specific than this.

During this time collisional and radiative effects lead to a significant reduction in the excited-state contamination of the target. (Lindsay 1996: 213)

34In this case there is probably very little genuine hedging. Those who are specialists in the field are expected to know what constitutes a significant reduction. There is consequently a certain in-group collusion, which allows the use of a vague quantifying expression, thus conforming to expected style, but whose value is known more precisely, if not exactly, by the discourse community to which it is addressed.

Conclusion

35By way of a brief conclusion, I would say that this study shows vague quantification to be an integral and essential element of the scientific journal article. As linguists interested in the way scientific discourse works, it is of utmost importance that we do not allow our understanding of vague quantification in the scientific journal article to remain vague.

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Bibliographie

Corpus

DeMartini, Edward E., Frank A. Parrish & Denise M. Ellis. 1996. Barotrauma-associated regurgitation of food: Implications for diet studies of Hawaiian pink snapper, pristipomoides filamentosus (family Lutjanidae)”. Fishery Bulletin 94-2, 250-256.

Lesser, Michael P. & Sarah Lewis. 1996. “Action spectrum for the eeffects of UV radiation on photosynthesis in the hermatypic coral pocillopora damicornis”. Marine Ecology Progress Series 134, 171-177.

Lindsay, B.G. et alii. 1996. “Charge transfer of 0.5-, 1.5-, and 5-keV protons with atomic oxygen: Absolute differential and integral cross sections”. Physical Review A 53-1, 212-218.

Shear, Jason B., Edward B. Brown & Watt W. Webb. 1996. “Multiphoton-excited fluorescence of fluorogen-labeled neurotransmitters”. Analytical Chemistry 68/10, 1778-1783.

Shelton, P.M.J. & E. Gaten. 1996. “Spatial resolution determined by electrophysiological measurement of acceptance angle in two species of benthic decapod crustacean”. Journal of the Marine Biology Association 76, 391-401.

Tapsak, Mark A., Guo Hong Wang, Krist Azizian & William P. Weber. 1996. “Quantitative determination of completely acetylated pentaerythritol and pentaerythritol oligomers by high-performance liquid chromatography”. Analytical Chemistry 68/10, 1685-1687.

References

Banks, David. 1994a. Writ in Water, Aspects of the Scientific Journal Article. Brest: ERLA, Université de Bretagne Occidentale.

Banks, David. 1994b. “Hedges and how to trim them”. In Brekke, Magnar, Øivin Andersen, Trine Dahl & Johan Myking (eds.), Applications and Implications of Current LSP Research, Vol. 2. Bergen, Norway: Fagbokforlaget, 587-592.

Channell, Joanna. 1990. “Precise and vague quantities in writing on economics”. In Nash, Walter (ed.), The Writing Scholar, Studies in Academic Discourse. Newbury Park, USA: Sage.

Channell, Joanna. 1994. Vague Language. Oxford: Oxford University Press.

Crompton, Peter. 1997. “Hedging in academic writing, some theoretical problems”. English for Specific Purposes 16/4, 271-287.

Dubois, Betty Lou. 1987. “‘Something on the order of around forty to forty-Four’: Imprecise numerical expressions in biomedical slide talks”. Language in Society 16-4, 527-541.

Grice, H.P. 1975. “Logic and conversation”. In Cole, P. & J.L. Morgan (eds.), Syntax and Semantics, Vol 3, Speech Acts. New York: Academic Press, 41-58.

Myers, Greg. 1996. “Strategic vagueness in academic writing”. In Ventola, Eija & Anna Mauranen (eds.), Academic Writing, Intercultural and Textual Issues. Amsterdam: John Benjamins, 3-17.

Powell, Mava Jo. 1985. “Purposive vagueness: An evaluative dimension of vague quantifying expressions”. Journal of Linguistics 21/1, 31-50.

Salager-Meyer, Françoise. 1994. “Hedges and textual communicative function in medical English written discourse”. English for Specific Purposes 13/2, 149-170.

Salager-Meyer, Françoise. 1995. “I think that perhaps you should: A study of hedges in written scientific discourse”. The Journal of TESOL France 2/2, 127-143.

Swales, John M. 1985. “English language papers and author’s first language: Preliminary explorations”. Scientometrics 8/1-2, 91-101.

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Notes

1 Articles in the corpus are identified by the first named author.

2 Highlighting in examples is mine throughout.

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Référence papier

David Banks, « Vague quantification in the scientific journal article », ASp, 19-22 | 1998, 17-27.

Référence électronique

David Banks, « Vague quantification in the scientific journal article », ASp [En ligne], 19-22 | 1998, mis en ligne le 17 février 2012, consulté le 28 juin 2017. URL : http://asp.revues.org/2666 ; DOI : 10.4000/asp.2666

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Auteur

David Banks

David Banks est maître de conférences à l’Université de Bretagne Occidentale où il enseigne la linguistique anglaise. Il est l’auteur de Writ in Water, Aspects of the Scientific Journal Article, ERLA, Université de Bretagne Occidentale ; il publie ESP France Newsletter. David.Banks@univ-brest.fr

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